Water surface profile along a side weir in a parabolic channel

A side weir is an overflow structure set into the side of a channel. This structure is used for water level control in channels, diverting excess water from a main channel into a side channel and as storm overflows from urban sewage systems. Computation of water surface profile over the side weirs is essential to determine the flow rate of the side weir. Discharge estimation of the side weir is still an important research subject. Most previous research works for the side weir were carried out in main channels with rectangular, triangular, trapezoidal and circular cross sections. Analytical solutions for water surface profile along a rectangular side weir are available only for the special cases of rectangular and trapezoidal main channels on the basis of a constant specific energy. No analytical solution is available for a rectangular side weir located in a parabolic channel. This research presents an elegant analytical solution for establishing the water surface profile along a side weir located in a parabolic channel which involves the use of incomplete elliptic integrals. The solution, which yields a direct computation, should be a useful computational tool for evaluation and design of rectangular side weirs in parabolic channels.